Question

DO NOT GIVE ME AN ANSWER! I WANT IT EXPLAINED REALLY SIMPLY! ONLY EXPLAIN AND HELP ME GET AN ANSWER NOT GIVE IT TO ME. :)

Answer 1

Which system of linear equations shares the same line?

A. 6x − 3y = 15
8x − 4y = 20

B. 6x − 2y = 2
x 1/3 + y = 1/3

C. 3x − 3y = 15
9x − 6y = 6

D. −4x + 4y = −4
2x + 2y = 2

Answer 2

I would proceed with elimination, and if I end up with 0=0, the two lines are coincident.
If I end up with 0=2, or something weird like that, then the two lines are parallel and distinct.

Answer 3

Your asking too much here lol

Answer 4

And I'm looking for ones that are, coincident?

Answer 5

Yes. Share the same line means they are sitting one on top of the other, or coincident.

Answer 6

I agree with @mathmate .... I'd just solve all of them for "y" and simplify
that'd show who is who

Answer 7

for each group check if one line is a multiple of the other
i got b because if you set the eqn in the form y = mx + b and simplify

Answer 8

Can someone show me for example with a how to solve them?

Answer 9

If you want to be lazy, (which I am), I would reject those where the slopes are clearly different.
For example, B and D have two lines with one line having a positive slope, and the other negative. They would not be candidates.

Answer 10

A. 6x − 3y = 15
8x − 4y = 20

If you see in A

3(2x - y) = 3(5) => 2x-y = 5
AND

4(2x-y) = 4(5) => 2x-y=5

So for these types of questions, spot which one has a common factor and see if there simplest forms are equal or not!

Understood? :) @CrazyCountryGirl

Answer 11

To be even more lazy, I would look at the coefficients.
If they are not in the same ratio, they cannot be parallel, and so they cannot be coincident.
That leaves you already with one choice.

Answer 12

To answer your question, I will solve B for you.

Answer 13

@CrazyCountryGirl do u understand wat i did for u

Answer 14

6x-2y=2
x/3+y=1/3
Multiply the second equation and add to the first:
6x-2y=2
2x/3+2y=2/3
--------------
20x/3 = 8/3
20x = 8
x=2/5
so the two lines cross each other, i.e. not coincident.

Answer 15

no reply yet @CrazyCountryGirl

Answer 16

Sorry, give me a minute. :)

Answer 17

Wait so it's A? If we're looking for the ones that have the same answer...

Answer 18

There you go!

Answer 19

exactly

Answer 20

So I'm going to see if I can figure this one out, don't help yet. :) Just tell me if I'm going in the right direction. :)

Which system of linear equations has no solution?

A. 2x − y = −1
2x + y = 2

B. 4x − y = 3
3x − 2y = 3

C. −2x + 4y = −16
4x − 2y = −1

D. 2x − y = −1
−2x + y = −1

B AND D ARE RULED OUT!

Answer 21

You are definitely in the right direction!

Answer 22

But there was a mistake in the choices.
Can you tell me why you ruled them out?

Answer 23

When there are no solutions, it means that they are parallel AND not distinct.
If you solve them, they would look like 2=8 or something ridiculous like that.
You look for two lines that are parallel, but are not coincident.

Answer 24

did you find my error in b

Answer 25

To give you a hint, A has two equations, both have coefficients of x>0, but the sign of coeff. of y are different, so they cannot be parallel. A can be ruled out.